The first rule of PAKE is: nobody ever wants to talk about PAKE. The second rule of PAKE is that this is a shame, because PAKE — which stands for Password Authenticated Key Exchange — is actually one of the most useful technologies that (almost) never gets used. It should be deployed everywhere, and yet it isn’t.

To understand why this is such a damn shame, let’s start by describing a very real problem.

Imagine I’m operating a server that has to store user passwords. The traditional way to do this is to hash each user password and store the result in a password database. There are many schools of thought on how to handle the hashing process; the most common recommendation these days is to use a memory-hard password hashing function like scrypt or argon2 (with a unique per-password salt), and then store only the hashed result. There are various arguments about which hash function to use, and whether it could help to also use some secret value (called “pepper“), but we’ll ignore these for the moment.

Regardless of the approach you take, all of these solutions have a single achilles heel:

When the user comes back to log into your website, they will still need to send over their (cleartext) password, since this is required in order for the server to do the check.

This requirement can lead to disaster if your server is ever persistently compromised, or if your developers make a simple mistake. For example, earlier this year Twitter asked all of its (330 million!) users to change their passwords — because it turned out that company had been logging cleartext (unhashed) passwords.

Now, the login problem doesn’t negate the advantage of password hashing in any way. But it does demand a better solution: one where the user’s password never has to go to the server in cleartext. The cryptographic tool that can give this to us is PAKE, and in particular a new protocol called OPAQUE, which I’ll get to at the end of this post.

What’s a PAKE?

A PAKE protocol, first introduced by Bellovin and Merritt, is a special form of cryptographic key exchange protocol. Key exchange (or “key agreement”) protocols are designed to help two parties (call them a client and server) agree on a shared key, using public-key cryptography. The earliest key exchange protocols — like classical Diffie-Hellman — were unauthenticated, which made them vulnerable to man-in-the-middle attacks. The distinguishing feature of PAKE protocols is the client will authenticate herself to the server using a password. For obvious reasons, the password, or a hash of it, is assumed to be already known to the server, which is what allows for checking.

If this was all we required, PAKE protocols would be easy to build. What makes a PAKE truly useful is that it should also provide protection for the client’s password. A stronger version of this guarantee can be stated as follows: after a login attempt (valid, or invalid) both the client and server should learn only whether the client’s password matched the server’s expected value, and no additional information. This is a powerful guarantee. In fact, it’s not dissimilar to what we ask for from a zero knowledge proof.

Of course, the obvious problem with PAKE is that many people don’t want to run a “key exchange” protocol in the first place! They just want to verify that a user knows a password.

The great thing about PAKE is that the simpler “login only” use-case is easy to achieve. If I have a standard PAKE protocol that allows a client and server to agree on a shared key K if (and only if) the client knows the right password, then all we need add is a simple check that both parties have arrived at the same key. (This can be done, for example, by having the parties compute some cryptographic function with it and check the results.) So PAKE is useful even if all you’ve got in mind is password checking.

SRP: The PAKE that Time Forgot

The PAKE concept seems like it provides an obvious security benefit when compared to the naive approach we use to log into servers today. And the techniques are old, in the sense that PAKEs have been known since way back in 1992! Despite this, they’ve seen from almost no adoption. What’s going on?

There are a few obvious reasons for this. The most obvious has to do with the limitations of the web: it’s much easier to put a password form onto a web page than it is to do fancy crypto in the browser. But this explanation isn’t sufficient. Even native applications rarely implement PAKE for their logins. Another potential explanation has to do with patents, though most of these are expired now. To me there are two likely reasons for the ongoing absence of PAKE: (1) there’s a lack of good PAKE implementations in useful languages, which makes it a hassle to use, and (2) cryptographers are bad at communicating the value of their work, so most people don’t know PAKE is even an option.

Even though I said PAKE isn’t deployed, there are some exceptions to the rule.

One of the remarkable ones is a 1998 protocol designed by Tom Wu [correction: not Tim Wu] and called “SRP”. Short for “Secure Remote Password“, this is a simple three-round PAKE with a few elegant features that were not found in the earliest works. Moreover, SRP has the distinction of being (as far as I know) the most widely-deployed PAKE protocol in the world. I cite two pieces of evidence for this claim:

1. SRP has been standardized as a TLS ciphersuite, and is actually implemented in libraries like OpenSSL, even though nobody seems to use it much.
2. Apple uses SRP extensively in their iCloud Key Vault.

This second fact by itself could make SRP one of the most widely used cryptographic protocols in the world, so vast is the number of devices that Apple ships. So this is nothing to sneer at.

Industry adoption of SRP is nice, but also kind of a bummer: mainly because while any PAKE adoption is cool, SRP itself isn’t the best PAKE we can deploy. I was planning to go into the weeds about why I feel so strongly about SRP, but it got longwinded and it distracted from the really nice protocol I actually want to talk about further below. If you’re still interested, I moved the discussion onto this page.

In lieu of those details, let me give a quick and dirty TL;DR on SRP:

1. SRP does some stuff “right”. For one thing, unlike early PAKEs it does not require you to store a raw password on the server (or, equivalently, a hash that could be used by a malicious client in place of the password). Instead, the server stores a “verifier” which is a one-way function of the password hash. This means a leak of the password database does not (immediately) allow the attacker to impersonate the user — unless they conduct further expensive dictionary attacks. (The technical name for this is “asymmetric” PAKE.)
2. Even better, the current version of SRP (v4 v6a) isn’t obviously broken!
3. However (and with no offense to the designers) the SRP protocol design is completely bonkers, and earlier versions have been broken several times — which is why we’re now at revision 6a. Plus the “security proof” in the original research paper doesn’t really prove anything meaningful.
4. SRP currently relies on integer (finite field) arithmetic, and for various reasons (see point 3 above) the construction is not obviously transferable to the elliptic curve setting. This requires more bandwidth and computation, and thus SRP can’t take advantage of the many efficiency improvements we’ve developed in settings like Curve25519.
5. SRP is vulnerable to pre-computation attacks, due to the fact that it hands over the user’s “salt” to any attacker who can start an SRP session. This means I can ask a server for your salt, and build a dictionary of potential password hashes even before the server is compromised.
6. Despite all these drawbacks, SRP is simple — and actually ships with working code. Plus there’s working code in OpenSSL that even integrates with TLS, which makes it relatively easy to adopt.

Out of all these points, the final one is almost certainly responsible for the (relatively) high degree of commercial success that SRP has seen when compared to other PAKE protocols. It’s not ideal, but it’s real. This is something for cryptographers to keep in mind.

OPAQUE: The PAKE of a new generation

When I started thinking about PAKEs a few months ago, I couldn’t help but notice that most of the existing work was kind of crummy. It either had weird problems like SRP, or it required the user to store the password (or an effective password) on the server, or it revealed the salt to an attacker — allowing pre-computation attacks.

Then earlier this year, Jarecki, Krawczyk and Xu proposed a new protocol called OPAQUE. Opaque has a number of extremely nice advantages:

1. It can be implemented in any setting where Diffie-Hellman and discrete log (type) problems are hard. This means that, unlike SRP, it can be easily instantiated using efficient elliptic curves.
2. Even better: OPAQUE does not reveal the salt to the attacker. It solves this problem by using an efficient “oblivious PRF” to combine the salt with the password, in a way that ensures the client does not learn the salt and the server does not learn the password.
3. OPAQUE works with any password hashing function. Even better, since all the hashing work is done on the client, OPAQUE can actually take load off the server, freeing an online service up to use much strong security settings — for example, configuring scrypt with large RAM parameters.
4. In terms of number of messages and exponentiations, OPAQUE is not much different from SRP. But since it can be implemented in more efficient settings, it’s likely to be a lot more efficient.
5. Unlike SRP, OPAQUE has a reasonable security proof (in a very strong model).

There’s even an Internet Draft proposal for OPAQUE, which you can read here. Unfortunately, at this point I’m not aware of any production quality implementations of the code (if you know of one, please link to it in the comments and I’ll update). (Update: There are several potential implementations listed in the comments — I haven’t looked closely enough to endorse any, but this is great!) But that should soon change.

The full OPAQUE protocol is given a little bit further below. In the rest of this section I’m going to go into the weeds on how OPAQUE works.

Problem 1: Keeping the salt secret. As I mentioned above, the main problem with earlier PAKEs is the need to transmit the salt from a server to a (so far unauthenticated) client. This enables an attacker to run pre-computation attacks, where they can build an offline dictionary based on this salt.

The challenge here is that the salt is typically fed into a hash function (like scrypt) along with the password. Intuitively someone has to compute that function. If it’s the server, then the server needs to see the password — which defeats the whole purpose. If it’s the client, then the client needs the salt.

In theory one could get around this problem by computing the password hashing function using secure two-party computation (2PC). In practice, solutions like this are almost certainly not going to be efficient — most notably because password hashing functions are designed to be complex and time consuming, which will basically explode the complexity of any 2PC system.

OPAQUE gets around this with the following clever trick. They leave the password hash on the client’s side, but they don’t feed it the stored salt. Instead, they use a special two-party protocol called an oblivious PRF to calculate a second salt (call it salt2) so that the client can use salt2 in the hash function — but does not learn the original salt.

The basic idea of such a function is that the server and client can jointly compute a function PRF(salt, password), where the server knows “salt” and the client knows “password”. Only the client learns the output of this function. Neither party learns anything about the other party’s input.

The gory details:

The actual implementation of the oblivious PRF relies on the idea that the client has the password and the server has the salt, which is expressed as a scalar value . The output of the PRF function should be of the form , where is a special hash function that hashes passwords into elements of a cyclic (prime-order) group.

To compute this PRF requires a protocol between the client and server. In this protocol, the client first computes and then “blinds” this password by selecting a random scalar value r, and blinding the result to obtain . At this point, the client can send the blinded value C over to the server, secure in the understanding that (in a prime-order group), the blinding by r hides all partial information about the underlying password.

The server, which has a salt value s, now further exponentiates this calue to obtain and sends the result R back to the client. If we write this out in detail, the result can be expressed as $R = H(P)^{rs}$. The client now computes the inverse of its own blinding value r and exponentiates one more time as follows: . This element , which consists of the hash of the password exponentiated by the salt, is the output of the desired PRF function.

A nice feature of this protocol is that, if the client enters the wrong password into the protocol, she should obtain a value that is very different from the actual value she wants. This guarantee comes from the fact that the hash function is likely to produce wildly different outputs for distinct passwords.

Problem 2: Proving that the client got the right key K. Of course, at this point, the client has derived a key K, but the server has no idea what it is. Nor does the server know whether it’s the right key.

The solution OPAQUE uses based an old idea due to Gentry, Mackenzie and Ramzan. When the user first registers with the server, she generates a strong public and private key for a secure agreement protocol (like HMQV), and encrypts the resulting private key under K, along with the server’s public key. The resulting authenticated ciphertext (and the public key) is stored in the password database.

C = Encrypt(K, client secret key | server’s public key)

When the client wishes to authenticate using the OPAQUE protocol, the server sends it the stored ciphertext C. If the client entered the right password into the first phase, she can derive K, and now decrypt this ciphertext. Otherwise it’s useless. Using the embedded secret key, she can now run a standard authenticated key agreement protocol to complete the handshake. (The server verifies the clients’ inputs against its copy of the client’s public key, and the client does similarly.)

Putting it all together. All of these different steps can be merged together into a single protocol that has the same number of rounds as SRP. Leaving aside the key verification steps, it looks like the protocol above. Basically, just two messages: one from the client and one returned to the server.

The final aspect of the OPAQUE work is that it includes a strong security proof that shows the resulting protocol can be proven secure under the 1-more discrete logarithm assumption in the random oracle model, which is a (well, relatively) standard assumption that appears to hold in the settings we work with.

In conclusion

So in summary, we have this neat technology that could make the process of using passwords much easier, and could allow us to do it in a much more efficient way — with larger hashing parameters, and more work done by the client? Why isn’t this everywhere?

Maybe in the next few years it will be.